alainjulius wrote:Find the equation of the ellipse given directrix at y = (9)(sqrt of 5)/5 + 2, center at (2, -6) and one of the vertices on (2, -4).

I did the graph. That's a good place to start. From the center and the one vertex, you know that the other vertex is at (2, -8), so the long axis is 4 units across and "a" is 2. The directrix for an ellipse is some constant-ratio (straight-line) distance from the nearby focal point as the focal point is (diagonally-ish) from the ellipse. (It's hard to say in words. The picture in that link is helpful.) The nearby focus is (2, c). That site in the second link says that the relationship is y = a^2/c = 4/c. So let's solve for c:

Hey, thanks for the reply. I just wanna ask how did you arrive on the equation 9(sqrt{5})/5 + 2 = 4/c?Also, I tried to solve for the c without actually looking at your solution and I didn't get to arrive at solving the c using quadratic formula. I cross-multiplied c to the left side so I end up with 4/9(sqrt[5])/5 and I solve for the c.I think it's algrebraically correct.And if just in case I'm wrong, what value would you choose between two C's, cause accdng to your solution we have two C values, right? thank you.